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Full text of "Analytical Mechanics"

IMPULSE AND MOMENTUM                      24$
and  TI = 0; on the other hand if the bodies are perfectly inelastic, 6 = 0; therefore, TI = f     *   2    (vi — v2]2.
201. Impact.—When the mass of one of the colliding bodies is very large compared with that of the other the velocity of the former with respect to the center of mass of the colliding system does not change appreciably during the collision. In such a case the body with the greater mass is considered to be fixed and the collision is called an impact-The impact of a falling body when it strikes the ground is a case in point.
The velocities of the larger mass before and after the collision, as well as the common velocity at the instant of maximum compression, are negligible. Therefore making these changes in the expressions for L, L', e, and Tl and. dropping the subscripts we obtain L = mv,
(X")
and                 .       Tl=^mv2(l-e2),                    (XI')
where m is the mass of the impinging body, while v and v' are its velocities just before and just after impact, respectively.
ILLUSTRATIVE   EXAMPLE.
A ball which is thrown vertically down from a height h rises to the point of projection after impinging against a horizontal floor. Find the velocity of projection and the loss in energy.
Let v0 be the velocity of projection, then the velocities just before and just after the impact are
v = VvQ2 + 2gh   and   v' — \/2gh, respectively.   But v' = ev.   Therefore